1. Holt Geometry 10-2-3 Arcs and Chords 10-2-3 Arc Measures and Chords Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Geometry 10-2-3 Arcs and Chords Apply properties of arcs. Apply properties of chords. Objectives

3. Holt Geometry 10-2-3 Arcs and Chords central anglesemicircle arcadjacent arcs minor arccongruent arcs major arc Vocabulary

4. Holt Geometry 10-2-3 Arcs and Chords A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.

5. Holt Geometry 10-2-3 Arcs and Chords

6. Holt Geometry 10-2-3 Arcs and Chords Minor arcs may be named by two points. Major arcs and semicircles must be named by three points. Writing Math

7. Holt Geometry 10-2-3 Arcs and Chords Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF. = 234 mKLF = 360 ° – mKJF mKJF = 0.35(360) = 126 mKLF = 360 ° – 126 °

8. Holt Geometry 10-2-3 Arcs and Chords Check It Out! Example 1 Use the graph to find each of the following. a. mFMC mFMC = 0.30(360) = 108 = 270 b. mAHB c. mEMD = 0.10(360) = 36= 360 ° – 0.25(360)mAHB = 360 ° – mAMB Central  is 30% of the . Central  is 10% of the .

9. Holt Geometry 10-2-3 Arcs and Chords Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

10. Holt Geometry 10-2-3 Arcs and Chords Example 2: Using the Arc Addition Postulate mCFD = 180 – (97.4 + 52) = 30.6 = 97.4 + 30.6 = 128 mBD = mBC + mCD mBC = 97.4 Vert.  s Thm. ∆ Sum Thm. m  CFD = 30.6  Arc Add. Post. Substitute. Simplify. Find mBD. mCD = 30.6

11. Holt Geometry 10-2-3 Arcs and Chords Check It Out! Example 2a Find each measure. mJKL mKPL = 180° – (40 + 25)° = 25° + 115° mKL = 115° mJKL = mJK + mKL = 140° Arc Add. Post. Substitute. Simplify.

12. Holt Geometry 10-2-3 Arcs and Chords Check It Out! Example 2b Find each measure. mLJN = 295° mLJN = 360° – (40 + 25)°

13. Holt Geometry 10-2-3 Arcs and Chords Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST  UV.

14. Holt Geometry 10-2-3 Arcs and Chords

15. Holt Geometry 10-2-3 Arcs and Chords Example 3A: Applying Congruent Angles, Arcs, and Chords TV  WS. Find mWS. 9n – 11 = 7n + 11 2n = 22 n = 11 = 88°  chords have  arcs. Def. of  arcs Substitute the given measures. Subtract 7n and add 11 to both sides. Divide both sides by 2. Substitute 11 for n. Simplify. mTV = mWS mWS = 7(11) + 11 TV  WS

16. Holt Geometry 10-2-3 Arcs and Chords Example 3B: Applying Congruent Angles, Arcs, and Chords  C   J, and mGCD  mNJM. Find NM. GD = NM  arcs have  chords. GD  NM  GCD   NJM Def. of  chords

17. Holt Geometry 10-2-3 Arcs and Chords Example 3B Continued 14t – 26 = 5t + 1 9t = 27 NM = 5(3) + 1 = 16 Substitute the given measures. Subtract 5t and add 26 to both sides. Divide both sides by 9. Simplify. t = 3 Substitute 3 for t.  C   J, and mGCD  mNJM. Find NM.

18. Holt Geometry 10-2-3 Arcs and Chords

19. Holt Geometry 10-2-3 Arcs and Chords Find NP. Example 4: Using Radii and Chords Step 2 Use the Pythagorean Theorem. Step 3 Find NP. RN = 17 Radii of a  are . SN 2 + RS 2 = RN 2 SN 2 + 8 2 = 17 2 SN 2 = 225 SN = 15 NP = 2(15) = 30 Substitute 8 for RS and 17 for RN. Subtract 8 2 from both sides. Take the square root of both sides. RM  NP, so RM bisects NP. Step 1 Draw radius RN.

20. Holt Geometry 10-2-3 Arcs and Chords Check It Out! Example 4 Find QR to the nearest tenth. Step 2 Use the Pythagorean Theorem. Step 3 Find QR. PQ = 20 Radii of a  are . TQ 2 + PT 2 = PQ 2 TQ 2 + 10 2 = 20 2 TQ 2 = 300 TQ  17.3 QR = 2(17.3) = 34.6 Substitute 10 for PT and 20 for PQ. Subtract 10 2 from both sides. Take the square root of both sides. PS  QR, so PS bisects QR. Step 1 Draw radius PQ.

21. Holt Geometry 10-2-3 Arcs and Chords Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find mTRQ. 158.4

22. Holt Geometry 10-2-3 Arcs and Chords Lesson Quiz: Part II 2. NGH 139 Find each measure. 3. HL 21

23. Holt Geometry 10-2-3 Arcs and Chords Lesson Quiz: Part III  12.9 4.  T   U, and AC = 47.2. Find PL to the nearest tenth.